OM3-1 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Chapter 3 Forecasting

OM3-2 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting FORECAST: A statement about the future Used to help managers –Plan the system –Plan the use of the system

OM3-3 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, MRP, workloads Product/service designNew products and services Uses of Forecasts

OM3-4 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases I see that you will get an A this semester.

OM3-5 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

OM3-6 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Gather and analyze data Step 5 Prepare the forecast Step 6 Monitor the forecast “The forecast”

OM3-7 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecast Accuracy Error - difference between actual value and predicted value Average Error (BIAS) – Any Problems! Mean absolute deviation (MAD) – Average absolute error Mean Absolute Percentage Error (MAPE) Mean squared error (MSE) – Average of squared error Tracking signal – Ratio of cumulative error and MAD

OM3-8 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting BIAS & MSE BIAS = Actualforecast )   n ( MSE = Actualforecast )   n (

OM3-9 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting MAD & MAPE MAD = Actualforecast   n MAPE = |Actual- Forecast| )/Actual  n (

OM3-10 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Types of Forecasts Judgmental - uses subjective inputs Time series - uses historical data assuming the future will be like the past Associative models - uses explanatory variables to predict the future

OM3-11 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Judgmental Forecasts Executive opinions Sales force composite Consumer surveys Focus Groups Outside opinion Opinions of managers and staff – Delphi technique

OM3-12 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Time Series Forecasts Trend - long-term movement in data Seasonality - short-term regular variations in data Irregular variations - caused by unusual circumstances Random variations - caused by chance

OM3-13 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecast Variations Trend Irregular variatio n Cycles Seasonal variations Figure 3-1

OM3-14 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Simple to use Virtually no cost Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy Naïve Forecasts

OM3-15 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Techniques for Averaging Naïve forecasts Arithmetic Mean Moving Averages Weighted Moving Averages Exponential Smoothing

OM3-16 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Definitions A t = Actual Demand in period t F t = Forecast Demand in period t n = Number of past Observations

OM3-17 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Stable time series data –F(t) = A(t-1) Seasonal variations –F(t) = A(t-n) Data with trends –F(t) = A(t-1) + (A(t-1) – A(t-2)) Uses for Naïve Forecasts

OM3-18 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Naive Forecasts Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

OM3-19 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Arithmetic Average F t+1 = n AiAi i = 1  n

OM3-20 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Techniques for Averaging Moving average Weighted moving average Exponential smoothing

OM3-21 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Simple Moving Average F t+1 = k AiAi i = 1  k Figure 3-4

OM3-22 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Weighted Moving Average F t+1 = A t *w t + A t-1 *w t-1 + A t-2 *w t-2 + ….+ A t-k *w t-k where:  w i = 1

OM3-23 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Exponential Smoothing n Premise--The most recent observations might have the highest predictive value. – Therefore, we should give more weight to the more recent time periods when forecasting. F t+1 = F t +  ( A t - F t ) Or F t+1 =  A t + (1-  F t

OM3-24 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Example 1 A laundry has experienced the following past demand pattern for garment cleaning. PeriodAnnual Demand (kgs)

OM3-25 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Example 1 (cont.) Forecast demand for period seven using: a)Last period demand b)The arithmetic average c)Three period moving average d)Weighted moving average with the weights as.2,.3, and.5 e)Exponential smoothing with  = 0.1

OM3-26 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Example of Picking a Smoothing Constant

OM3-27 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Picking a Smoothing Constant .1 .4 Actual

OM3-28 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Common Nonlinear Trends Parabolic Exponential Growth Figure 3-5

OM3-29 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Equation b is similar to the slope. However, since it is calculated with the variability of the data in mind, its formulation is not as straight-forward as our usual notion of slope. Y t = a + bt t Y

OM3-30 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Calculating a and b b = n(ty) - ty nt 2 - ( t) 2 a = y - bt n   

OM3-31 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Equation Example

OM3-32 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Trend Calculation y = t a= (15) 5 = b= 5 (2499)- 15(812) 5(55)- 225 = =

OM3-33 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecasting: Trend Adjustment Example 2

OM3-34 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Solution Example 2 (a) - Trend Equation Using Excel, the following can be obtained as the best fit line for Example 2 (a). Y = t

OM3-35 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecasting: Seasonal Adjustments Seasonal Variations are regularly repeating upward or downward movements in series values that can be tied to recurring events. Examples include winter and summer clothing, ski equipment, rush hour traffic, restaurants, and customer service assistance. Additive vs. Multiplicative Models

OM3-36 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecasting: Seasonal Adjustments Use multiplicative method known as Ratio-to-Trend Method Actual Observation Trend Value

OM3-37 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Forecasting: Seasonal Adjustments Use the linear regression model to capture the trend component and forecast each past period. Divide the actual observation by the trend value to obtain a ratio. Average ratios of similar periods to obtain seasonal factors. Multiply the trend forecasted value by the appropriate seasonal factors to obtain seasonally adjusted forecasts. See example 2 (b)

OM3-38 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting Predictor variables - used to predict values of variable interest Regression - technique for fitting a line to a set of points Least squares line - minimizes sum of squared deviations around the line

OM3-39 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting Again, the least squares line equation is used: y = a + b(x) where, y = Predicted (dependent) variable x = Predictor (independent) variable b = Slope of the line a = Value of y, when x=0 (or the y intercept)

OM3-40 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting Then,

OM3-41 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting Coefficient of Correlation (r): The coefficient of correlation r is a relative measure of such a relationship between two variables. Coefficient of Determination (r 2 ) It is a statistic that indicates how well a regression line explains or fits the observed data. -1 < r < +1 r > 0 implies positive correlation r < 0 implies negative correlation

OM3-42 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting -1 < r < +1 r > 0 implies positive correlation r < 0 implies negative correlation R can be calculated by using the following equation:

OM3-43 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Associative Forecasting Control Limits on the Forecast Value Upper Limit = Forecast Value + z (S yx ) Lower Limit = Forecast Value – z (S yx ) where, z is the standard normal deviate and

OM3-44 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Linear Model Seems Reasonable Computed relationship

OM3-45 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Tracking Signal Tracking Signal is a measurement that indicates whether the forecast average is keeping pace with any genuine upward or downward changes in demand

OM3-46 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Tracking Signal Tracking signal = ( Actual - forecast ) MAD  Tracking signal = ( Actual - forecast) Actual - forecast   n

OM3-47 McGraw-Hill/Irwin Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. Forecasting Tracking Signal Example